" 10."int_(0)^((pi)/(2))(2log sin x-log sin2x)dx

int_(0)^((pi)/(2))(2log cos x-log sin2x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(2log sin x-log sin2x)dx

int_(0)^((pi)/(2))log(sin x)dx

int_(0)^(pi//2) (2logsin x - log sin 2x) dx=

int_(0)^((pi)/(2))log(sin2x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(2log sin x - log sin 2x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(2log sin x log sin 2x)dx

Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx and hence evaluate int_(0)^(pi//2)(2log sin x-log sin2x)dx .